Implicit Differentiation

Implicit Differentiation

If:

$$F(x,y)=0$$

then differentiating with respect to $$x$$ gives:

$$\frac{\partial F}{\partial x}+\frac{\partial F}{\partial y}\frac{dy}{dx}=0$$

Hence:

$$\frac{dy}{dx}=-\frac{F_x}{F_y}$$

provided:

$$F_y\neq0$$

Usage

- Used when $$y$$ is not explicitly expressed as a function of $$x$$.